Analytical Solutions for a Supersymmetric Wave‐Equation for Quasiparticles in a Quantum System

2019 ◽  
Vol 3 (1) ◽  
pp. 1900173 ◽  
Author(s):  
Sergio Manzetti ◽  
Alexander Trounev
Keyword(s):  
Wave Equation ◽  
Quantum System ◽  
Analytical Solutions

scholarly journals New Analytical Solutions of Fractional Symmetric Regularized-Long-Wave Equation

2020 ◽  
Vol 66 (3 May-Jun) ◽  
pp. 297
Author(s):  
Mehmet Senol
Keyword(s):  
Wave Equation ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Algebraic Method ◽  
Symbolic Calculation ◽  
Solution Sets ◽  
Flow Models ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Fractional Differential

In this study, new extended direct algebraic method is successfully implemented to acquire new exact wave solution sets for symmetric regularized-long-wave (SRLW) equation which arise in long water flow models. By the help of Mathematica symbolic calculation package, the method produced a great number of analytical solutions. We also presented a few graphical illustrations for some surfaces. The fractional derivatives are considered in the conformable sense. All of the solutions were checked by substitution to ensure the reliability of the method. Obtained results confirm that the method is straightforward, powerful and effective method to attain exact solutions for nonlinear fractional differential equations. Therefore, the method is a good candidate to take part in the existing literature.

Exact solutions of a quartic potential

2019 ◽  
Vol 34 (26) ◽  
pp. 1950208 ◽  
Author(s):  
Qian Dong ◽  
Guo-Hua Sun ◽  
M. Avila Aoki ◽  
Chang-Yuan Chen ◽  
Shi-Hai Dong
Keyword(s):  
Exact Solutions ◽  
Quantum System ◽  
Analytical Solutions ◽  
Wave Functions ◽  
Negative Potential ◽  
Potential Parameter ◽  
Real Numbers ◽  
Quartic Potential ◽  
Heun Functions ◽  
Potential Parameters

We find that the analytical solutions to quantum system with a quartic potential [Formula: see text] (arbitrary [Formula: see text] and [Formula: see text] are real numbers) are given by the triconfluent Heun functions [Formula: see text]. The properties of the wave functions, which are strongly relevant for the potential parameters [Formula: see text] and [Formula: see text], are illustrated. It is shown that the wave functions are shrunk to the origin for a given [Formula: see text] when the potential parameter [Formula: see text] increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter [Formula: see text] increases or parameter [Formula: see text] decreases for a given negative potential parameter [Formula: see text]. The minimum value of the double well case ([Formula: see text]) is given by [Formula: see text] at [Formula: see text].

scholarly journals New analytical Solutions of (3+1)-dimensional Shallow Water Wave equation (SWW)

2021 ◽  
Vol 12 (2) ◽  
pp. 3036-3038
Author(s):  
Anjali Verma, Et. al.
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Analytical Solutions ◽  
Water Wave ◽  
Wave Theory ◽  
Shallow Water Wave ◽  
Kudryashov Method ◽  
Calculation Software

In this paper, we have obtained new analytical solutions of (3+1)-dimensional SWW equation with Kudryashov method. The study of Shallow water wave equation plays an imperative role in wave theory. For calculation software Maple is used. The solutions obtained by this method are new.  

scholarly journals Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 597 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Wave Equation ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Wave Equations ◽  
Analytical Techniques ◽  
Nonlinear Problems ◽  
High Rate ◽  
Numerical Examples ◽  
Linear And Nonlinear

In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure of natural transform decomposition method. The natural transform decomposition method procedure has shown that less volume of calculations and a high rate of convergence can be easily applied to other nonlinear problems. Therefore, the natural transform decomposition method is considered to be one of the best analytical techniques, in order to solve fractional-order linear and nonlinear Partial deferential equations, particularly fractional-order heat and wave equation.

scholarly journals Abundant Wave Accurate Analytical Solutions of the Fractional Nonlinear Hirota–Satsuma–Shallow Water Wave Equation

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 235
Author(s):  
Chen Yue ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Shallow Water ◽  
Analytical Solutions ◽  
Water Wave ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Conformable Fractional Derivative ◽  
Adomian Decomposition ◽  
Fractional System

This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable fractional derivative is employed to convert the fractional system into a system with an integer–order. The extended simplest equation (ESE) and modified Kudryashov (MKud) methods are used to construct novel solutions of the considered model. The solutions’ accuracy is investigated by handling the computational solutions with the Adomian decomposition method. The solutions are explained in some different sketches to demonstrate more novel properties of the considered model.

scholarly journals Quantum information for a solitonic particle with hyperbolic interaction

2021 ◽  
Author(s):  
Allan Ranieri Pereira Moreira
Keyword(s):  
Quantum Information ◽  
Kinetic Energy ◽  
Quantum System ◽  
Fisher Information ◽  
Analytical Solutions ◽  
Hamiltonian Operator ◽  
Barrier Potential ◽  
Stationary Quantum ◽  
Dependent Mass ◽  
Position Dependent Mass

Abstract In this work, we analyze a particle with position-dependent mass, with solitonic mass distribution in a stationary quantum system, for the particular case of the BenDaniel-Duke ordering, in a hyperbolic barrier potential. The kinetic energy ordering of BenDaniel-Duke guarantees the hermiticity of the Hamiltonian operator. We find the analytical solutions of the Schrödinger equation and their respective quantized energies. In addition, we calculate the Shannon entropy and Fisher information for the solutions in the case of the lowest energy states of the system.

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